Syllabus ( MATH 447 )

Basic information


Course title: 
Tensor Analysis 
Course code: 
MATH 447 
Lecturer: 
Prof. Dr. Oğul ESEN

ECTS credits: 
5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
4, Fall and Spring 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Departmental Elective

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
Math 113 
Professional practice: 
No 
Purpose of the course: 
Teach the basic concepts of tensor calculus and it’s applications in physics and applied mathematics. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Build up a solid background of tensor calculus.
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Ability to work in interdisciplinary research teams effectively.
Method of assessment

Term paper

Use the basic concepts of applied mathematics
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Exhibiting professional and ethical responsibility.
Method of assessment

Term paper

The students learn the application of Tensors which are the most important tools for the concept of Invariance.
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Written exam


Contents


Week 1: 
The concept of invariance, physical transformations and the concept of invariant equations. 
Week 2: 
Translational and rotational transformations. 
Week 3: 
Lorentz transformations and the broken invariance of Newton equation under Lorentz transformations. 
Week 4: 
Scalar invariants under these transformations. The infinitesimal arc length and its basis situation for tensorel calculations. 
Week 5: 
Vectors and their invariance principles. 2nd order and higher order tensors. 
Week 6: 
Maxwell equations and their invariance under Lorentz transformations. 
Week 7: 
Relativistic electrodynamics and its formalism. 
Week 8: 
Midterm Exam and solutions 
Week 9: 
Riemannian geometry and its principal tensors, Ricci, Riemann tensors 
Week 10: 
Einstein field equations and general relativity as a tensorel theory. 
Week 11: 
Various examples to the solutions of Einstein field equations. 
Week 12: 
Main solution techniques and the analysis of general relativity. 
Week 13: 
Lagrange theory of fields and writing invariant action functional. The application of tensors to physical sciences. 
Week 14: 
Invariant field theories and their difference from coordinate based theories. 
Week 15*: 
 
Week 16*: 
Final exam 
Textbooks and materials: 
General Relativity, Robert M. Wald, The University of Chicago Press, 1984 A Short Course in General Relativity, J. Foster, J. D. Nightingale, SpringerVerlag, 1995 
Recommended readings: 
Mathematical Methods for Physicists (Weber and Arfken) Tensors, Differential Forms and Variational Principles (David Lovelock and Hanno Rund) Tensor Analysis for Physicists (J. A. Schouten)


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
8 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
2 
14 

Practice, Recitation: 
0 
0 

Homework: 
0 
0 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
10 
1 

Midterm: 
3 
1 

Personal studies for final exam: 
10 
4 

Final exam: 
3 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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